A first degree homogeneous yield function is completely determined by its restriction to the unit sphere of the stress space; if, in addition, the function is isotropic and pressure independent, its restriction to the octahedric unit circle, the π-circle, is periodic and determines uniquely the function. Thus any homogeneous, isotropic and pressure independent yield function can be represented by the Fourier series of its π-circle restriction. Combinations of isotropic functions and linear transformations can then be used to extend the theory to anisotropic convex functions. The capabilities of this simple, yet quite general methodology are illustrated in the modeling of the yielding properties of AZ31B magnesium alloy.
Soare, S. C., & Benzerga, A. A. (2016). On the modeling of asymmetric yield functions. International Journal of Solids and Structures, 80, 486–500. https://doi.org/10.1016/j.ijsolstr.2015.10.009